Both the observation of a sizable transverse flow in holographic simulations of localized shock collisions and the need to consider transverse energy density fluctuations, to explain the observed large event-by-event fluctuations of flow observables during heavy ion collision, motivate to study collisions of projectiles with a realistic granular, transverse structure. Ideally one would want to simulate numerous such collisions for statistical analysis. This and higher transverse resolution required to account for transverse energy density fluctuations is computationally challenging. In order to make this feasible, I introduce a framework to simplify the simulation of the collision of localized shocks in five dimensional Anti-de Sitter space. By expanding the Einstein equations in transverse gradients one finds that already at first order numerical results agree well with the exact solutions. For the price of an error reaching 10% at the hydrodynamization time, the numerics can be sped up by roughly one order of magnitude. I also briefly discuss work towards the geometrization of turbulent fluid dynamics.